Conversational recommendation systems (CRS) leverage contextual information from conversations to generate recommendations but often struggle due to a lack of collaborative filtering (CF) signals, which capture user-item interaction patterns essential for accurate recommendations. We introduce Reddit-ML32M, a dataset that links Reddit conversations with interactions on MovieLens 32M, to enrich item representations by leveraging collaborative knowledge and addressing interaction sparsity in conversational datasets. We propose an LLM-based framework that uses Reddit-ML32M to align LLM-generated recommendations with CF embeddings, refining rankings for better performance. We evaluate our framework against three sets of baselines: CF-based recommenders using only interactions from CRS tasks, traditional CRS models, and LLM-based methods relying on conversational context without item representations. Our approach achieves consistent improvements, including a 12.32% increase in Hit Rate and a 9.9% improvement in NDCG, outperforming the best-performing baseline that relies on conversational context but lacks collaborative item representations.